An introduction to incidence matrices
Categories: Computer Science, MathematicsGiven a graph 
, with 
, 
, we can define a matrix 
, called 
's incidence matrix, defined as such:
![\[
B_{i, j} = \begin{cases}
1, \text{ if edge} j \text{ is incident to node } i\\
0, \text{otherwise}
\end{cases}
\]](/static/latex/7bb9441c1cfe29e6d6382af5351eebc8.png "\[
B_{i, j} = \begin{cases}
1, \text{ if edge} j \text{ is incident to node } i\\
0, \text{otherwise}
\end{cases}
\]")
In this post, we study some of this matrix's algebraic properties.
Algebraic aspects of adjacency matrices
Categories: Computer Science, MathematicsGiven a graph , with , , we can consider the matrix 
defined as such:
![\[
A_{i, j} = \begin{cases}
1, \text{ if } (v_i, v_j) \in E\\
0, \text{ otherwise }
\end{cases}
\]](/static/latex/ef3d7c630e41268c7409b7023fb7ff35.png "\[
A_{i, j} = \begin{cases}
1, \text{ if } (v_i, v_j) \in E\\
0, \text{ otherwise }
\end{cases}
\]")
We call this the adjacency matrix. In this article we study some of its algebraic properties.
Properties of graph representations
Categories: Programming, Mathematics, Computer ScienceWith the incredible usefulness of graphs and the amount of algorithms to solve graph problems, it is an important issue how we represent these graphs. In this post I will introduce a couple of ways of representing graphs on a computer, together with their advantages and disadvantages. In following posts I will discuss the interesting algebraic properties of the adjacency matrix, as well as some more advanced ways of representing graphs.
We'll turn to the two most used ones: adjacency matrices and adjacency lists. These are the "canonical" way of representing graphs. Both are quite simple data structures, yet ...
Maps
Categories: Functional Programming, Computer ScienceIn this post I'll talk a bit about the functional programming technique called map.
The basic definition of it is easy enough: For every type a, b, given a list X of elements of type a, and a function f taking a and returning b, map f X gives you a list Y of elements of type b, where the i-th element of Y is the result of applying f to the i-th element of X.
Above the fold
Categories: Functional Programming, Computer ScienceToday I'd like to talk a bit about one of the most common operations in functional programming, a fold.